Zhao Juanxia, Wang Yinhe, Gao Peitao, Li Shengping, Peng Yi
School of Automation, Guangdong University of Technology, Guangzhou 510006, China.
School of Electronics and Information, Guangdong Polytechnic Normal University, Guangzhou 510665, China.
Entropy (Basel). 2023 Oct 17;25(10):1457. doi: 10.3390/e25101457.
The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network's topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.
研究了具有随机链路动态特性的复杂动态网络（CDN）的均方同步问题。与以往文献不同，本文所考虑的CDN可视为由两个相互耦合的子系统组成。一个子系统由所有节点组成，称为节点子系统，另一个由所有链路组成，称为网络拓扑子系统，其中加权值可以定量反映网络拓扑的变化。基于对CDN的上述理解，分别使用两个带有布朗运动的向量随机微分方程来对节点和链路的动态行为进行建模。控制策略不仅包含节点中的控制器，还包含链路中的耦合项，通过该策略，CDN在均方意义下实现同步。同时，本文提出了动态随机信号，将其视为链路的辅助参考跟踪目标，使得当节点实现同步时，链路能够渐近跟踪参考目标。这意味着CDN最终的拓扑结构是随机的。最后，一个对比仿真例子证实了本文控制策略的优越性。
